Obviously this poor woman is doing her best to serve the Church. Perhaps, even in her own mind, she might be considering retiring from service - God only knows, it’s been her whole life’s service to God.
As someone in charge of music at my own parish, I understand what you’re going through. We had a gentleman in our choir with COPD. Eventually, he had to make use of an oxygen tank. I allowed him to carry on. I didn’t see it as an interruption. He couldn’t sing well at this point, but he blended with the tenors. Eventually he came to me and said “Is it alright with you if I retire from the choir? I can no longer sing to expectation.”
I was broken-hearted. I told him that, with someone in such a state, I had no expectation for him to be perfect. The priest thanked him for his service, and we agreed in fulness of love to tell him that if he ever felt strong enough to just don his cassock and surplice, and join us on Sunday. I had to give him a hug, and I accepted his resignation. A couple of times, he did join us, and goodness, was I happy to see him! To see this devotion to singing during the liturgy, to see this love of God and His Church. Touching.
OP, you could talk to this belching lady. But speak to her in a caring way, an interested way. Ask her how she’s doing, joke with her, tell her something that will make you and her laugh. Then, ask how her health is. Say you noticed that her demeanour was a bit off, or the spark in her eye was lost amongst the stars. Tell her how much you appreciate her singing, but you’re worried about her health, reputation, and that you don’t want her to suffer nor feel obligated to do something she doesn’t need to do anymore. Ask if she wants to leave the choir, and if she doesn’t, then tell her you will do everything to make sure she is appreciated by the rest of the choir and congregation.
Love goes a long way. However, so does discipline for the sake of beauty.